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Quantum Turing machine and brain model represented by Fock space. (English) Zbl 1351.81037

Summary: The adaptive dynamics is known as a new mathematics to treat with a complex phenomena, for example, chaos, quantum algorithm and psychological phenomena. In this paper, we briefly review the notion of the adaptive dynamics, and explain the definition of the generalized Turing machine (GTM) and recognition process represented by the Fock space. Moreover, we show that there exists the quantum channel which is described by the GKSL master equation to achieve the Chaos Amplifier used in [M. Ohya and I. V. Volovich, Rep. Math. Phys. 52, No. 1, 25–33 (2003; Zbl 1053.81014); “Quantum computing and the chaotic amplifier”, J Opt. B: Quant. Semiclass. Opt. 5, No. 6, 639–642 (2003; doi:10.1088/1464-4266/5/6/015)].

MSC:

81P68 Quantum computation
68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
68Q05 Models of computation (Turing machines, etc.) (MSC2010)
03D10 Turing machines and related notions

Citations:

Zbl 1053.81014
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Full Text: DOI

References:

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